[MITgcm-support] CFL condition for a Spherical Case

[Martin Losch]

Benjamin,

the most important constraint is the CFL number u*dt/dx < 1 (or 1/2) for stable explicit schemes. For that you need indeed the expected current velocity u, but since your are probably simulating an ocean system without surface gravity waves, you can probably estimate how large u will be, e.g. 1m/s is already quite fast. For a spherical (latlon) grid, you need use the smallest grid cell, i.e. the one closes to the poles, because dx = R*delta(phi)*cos(theta) for these grids. And then you have to test and find out how large your time step can be before the model explodes due the violation of the CFL criterion. The monitor output contains number that help in the process (advcfl_uvel_max, etc.), so it’s a good idea to have monitor output very often (even each timestep) in this testing phase.

At low resolution, it is usually possible to choose an A_h that is small enough to not violate the criteria that you mentioned, but at the same time high enough to make the grid resolve the flow (and make it stable). The criteria for A_h can be difficult at high resolution; in that case I recommend the scaled parameters viscAhgrid, which need to be below 1 (to satisfy the stability criterion). They are then scaled by the grid step and the time step; see mom_calc_visc.F for more details, or the documentation <http://mitgcm.org/public/r2_manual/latest/online_documents/node86.htm>

Martin

> On 09 Mar 2016, at 23:33, Benjamin Ocampo <rurik at ualberta.ca> wrote:
> 
> Hi All:
> 
> I have some questions about setting the resolution of the runs in a spherical polar case:
> 
> For the latitude (phi) and longitude (theta) coordinate system, there is a constraint (CFL) for how small I can make the grid-size for both phi and theta defined below where delta(phi) denotes the grid-size of phi:
> 
>    A_h < (R^2 delta(theta)^2)/(2 delta(t))
> 
>    A_h < (R^2 delta(phi)^2)/(2 delta(t))
> 
> where R is the radius of the planet.
> 
> 1) Is there another condition I can use that provides a maximum to the size of both delta(theta) and delta(phi)? 
> 
> The one I have read up on is the Reynold's number method but that assumes that I know the horizontal velocity scale beforehand.
> 
> I want to determine how low I can make the resolution in my spherical polar runs such that the model will resolve at minimum computation cost.
> 
> Cheers,
> Benjamin
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